Resizing of digital images is often performed in digital imaging processing and becomes more important in networks environments that include devices with different dpi resolution. While aliasing and moiré artifacts are the main problems in image reduction, enlargement of images has to deal with the problem of how to introduce high frequency components in order to have the image, in particular edges, not appear too smooth or too blurred. A typical method for enlargement of images is the use of an interpolation filter. This filtering incorporates information from neighboring pixels in order to predict an interpolation value. Commonly used filters as, e.g., in a popular photo-image manipulation application, are bilinear or bicubic interpolation filters. With the use of those filters a perfect step edge cannot be interpolated to produce a perfect step edge at a higher resolution. The interpolated edge will always look a bit blurred.
A standard method for image interpolation is polynomial interpolation. Depending on the degree of the interpolating polynomial (e.g., linear, quadratic, cubic, etc.), the image looks more or less smooth. The most commonly used technique is referred to as cubic interpolation. An advantage of polynomial methods is their simplicity since they are based on global linear filtering techniques. A disadvantage is that it is not possible to perform an adaptive interpolation, thereby resulting in edges typically being oversmoothed. This is a significant disadvantage in enlargement of documents.
Other interpolation filters exist, such as Keys filters, that are relatives of polynomial interpolation filters, but have characteristics of unsharp masking filters, i.e. they enhance high frequency content by creating a overshoot-undershoot at edges and an overshoot-undershoot is also created for noise pixel and leads to increase the noise level in the image. Since all these filters operate globally on the entire image, adaptive interpolation is not possible. A trade-off exists between enhancement of edges and suppressing noise in background areas.
Non-linear interpolation methods exist that operate in the pixel domain and extract edge information from the image and use that information to perform an edge-directed interpolation. One method first computes an edge map of the low resolution image using the Laplacian-of-Gaussian. In a second step, a preprocessing of the low resolution image using the edge information is performed to avoid errors in an estimated high resolution edge map. The third step performs interpolation using the edge information. In smooth areas, a bilinear interpolation is performed. Near edges, interpolated values are replaced by values that keep the sharpness of the edges. At last, an iterative correction step is performed to further improve the interpolation. A typical number of iterations is 10. See Allebach, J., and Wong, P. W., “Edge-directed interpolation,” Proceedings of ICIP'98, pp. 707–710, 1998.
In another method, local covariance characteristics in the low resolution image are estimated and those estimates are used to perform classical Wiener filtering interpolation. Since local covariances are part of the filter coefficients, a smoothing along edges, but not across edges, is performed. A disadvantage of this method is that isolated dots are not well-preserved after interpolation since they are treated as very short edges. See Li, X., and Orchard, M., “New edge directed interpolation,” Proceedings of ICIP'2000, Vancouver, 2000.
Compared to the previous two methods, a very simple edge sensitive interpolation method is proposed in Carrato, S., Ramponi, G., and Marsi. S., “A simple edge-sensitive image interpolation filter,” Proceedings of ICIP'96, pp. 711–714, 1996. This technique employs a nonlinear filter to determine the interpolating sample value. In detail, for a one-dimensional signal a local linear interpolation,xint=μkxk+(1−μk)xk+1  (1)is performed. If xint is close to 0, the interpolating value is similar to the sample to the right, whereas if xint is close to 1, the interpolating value is similar to the sample to the left. This placement depends on the smoothness of the low resolution signal in a neighborhood of the interpolating value and is computed via the nonlinearity
                              μ          k                =                                            k              ⁡                              (                                                      x                                          k                      +                      1                                                        -                                      x                                          k                      +                      2                                                                      )                                      -            1                                              k              (                                                                    (                                                                  x                                                  k                          -                          1                                                                    -                                              x                        k                                                              )                                    2                                +                                                      (                                                                  x                                                  k                          +                          1                                                                    -                                              x                                                  k                          +                          2                                                                                      )                                    2                                            )                        +            2                                              (        2        )            where k is a parameter that controls the edge sensitivity. For k=0, linear interpolation is obtained, while positive values of k cause increased edge sensitivity. An advantage of this nonlinear technique is its simplicity—no iterations are necessary. A disadvantage of this technique is that the parameter k must be tuned and that isolated short edges do not get enlarged and look a bit “squeezed” in the interpolated image. Furthermore, the interpolation of a perfect step edge, e.g., xk−1=xk=1, xk+1=xk+2=0, is not a perfect step edge anymore: 1, 1, 1, 1/2, 0, 0, 0. A linear interpolation is performed.
FIG. 1 is a schematic diagram illustrating a two-dimensional extension of one-dimensional nonlinear interpolation methods. The pixel locations containing “o” in FIG. 1 are representative of pixels of the low resolution image. An extension to two dimensions is performed by applying the one-dimensional method separately to rows and columns of the low resolution image Ilow, shown in matrix 101, with the results combined into Icomb, shown in matrix 102. The missing values are interpolated as averages of interpolation on rows and columns in the combined image Iint, shown in matrix 103.
Several techniques exist that explore multiresolution structures of images in the wavelet domain to extrapolate images. A general approach to edge preserving image interpolation with wavelets is to add an additional high frequency band to the wavelet decomposition of the low resolution image. Some prior art techniques determine the location of an edge by extrapolating extrema of wavelet coefficients across scales, or decomposition levels. This extrapolation typically requires a localization and a least-square fit of the extremes. A problem with those approaches is that the alignment of an edge is never sufficient. For extrapolating smoother images, it is less significant, but rather severe for extrapolation of text. One way to overcome this problem includes iterating on the extrapolation in order to better map the downsampled high resolution image to the original low resolution image. For more information, see Carey, W. K., Chuang, D. B., and Hemami, S. S., “Regularity-Preserving Image Interpolation,” Trans. Image Processing, vol. 8, no. 9, pp. 1293–1297, 1999 and Chang, S. G., Cvetkovic, Z., and Vetterli, M., “Resolution enhancement of images using wavelet transform extrema extrapolation,” Proceedings of ICASSP'95, pp. 2379–2382, 1995.
In U.S. Pat. No. 5,717,789, entitled, “Image enhancement by non-linear extrapolation in frequency space,”, issued February 1998, the Laplacian Pyramid is used to perform a modified unsharp masking on a smoothly interpolated image. In this case, it is difficult to align a perfect edge appropriately in the interpolated image.